A geographic information system (GIS) is a system for capturing, storing, analyzing, and managing data and associated attributes, which are spatially referenced to the earth. More generically, a GIS is a tool (e.g., a computer system) that allows users to interact with geographically-referenced information. Spatially referenced features (e.g., countries, rivers, lakes, cities, etc.) can be rendered by a GIS to provide a user with an interactive map.
Coordinate systems are used as references for the locations of spatial features that are represented in a GIS. For any given location on the Earth and for a given map display and scale, one or many of the more than 300 geographic coordinate systems and more than 2,500 projected coordinate systems can be applied. A geographic coordinate system specifies a location on the Earth using three coordinates of a spherical coordinate system aligned with the sign axis of the Earth.
A projection is a two-dimensional representation of a three-dimensional area, and a projection may be implemented using any of the projected coordinate systems. The projected coordinate system defines one or more mathematical functions to translate the three-dimensional representation to a two-dimensional representation. For example, a projection may be used to represent the Earth, a three-dimensional object, as a planar surface such as a rendered map in a GIS.
Properties of the Earth's surface can be measured independent of their geography. Examples of properties include area, shape, direction, distance, and scale. Map projections can be configured to preserve one or more of these properties, though not all of them simultaneously. Each projected coordinate system and the resulting map projection, preserves, compromises, or approximates the basic properties in different ways. The purpose of the map, then, determines which projected coordinate system should be utilized to generate the map projection.
FIG. 1 shows a typical map projection 100. FIG. 2 shows a polar projection 200. Polar projections 200 are highly distorted and stretched for areas away from the pole. This distortion presents a problem for reprojection of imagery. A typical image reprojection process uses the following steps:    1. Acquire a source image at a resolution (i.e. number of pixels) that is close to the desired output image.    2. Create an empty output image.    3. For each pixel in the output image:            a. Find the corresponding pixel location from the source image.        b. Using an interpolation method, generate a new pixel value from the area surrounding the source location.        c. Store that pixel value in the output image.        
Once completed, a completely reprojected output image is obtained. The technique outlined above works well for most projections, even those with significant distortion; however, for polar projections this technique will create highly distorted projected imagery. In FIG. 2, the area in the center of the image is the North Pole 202. Outward from the center 202 are areas of lower latitude, and a result of the polar projection is that areas of lower latitude are stretched relative to areas around the center 202. Area stretching can be up to a factor of two for areas near the equator 204.